You'd think nuking one city would have been enough for that...
The Americans didn't have to nuke any cities to test the nuclear bomb, they had already measured it's destructive capacity in the dessert. There is a belief among some historians that dropping the bomb was a way to impress the USSR and this idea does have merit.
As for the second bomb, the US only dropped the second one when the first one failed to elicit the response they desired. Japanese scientists were actually further along in designing their own weapon than the Nazi's were. They had a notion that the bomb was incredibly expensive to make and were gambling that the US couldn't make another.
Is there any evidence of that? Any official communication inside the Japanese government?
The Japanese strategy, once it became clear they were losing the war, was to increase the cost in order to force concessions from the Allies. The atomic bomb, by changing the equation to one plane, one bomb, one city destroyed that hope.
The Japanese high command didn't surrender because they lost two more cities, they surrendered because the US demonstrated that it could annihilate cities without giving any opportunity to strike back.
For better or worse, wars aren't won by killing people, they're won by killing hope.
There are always options. The simplest argument to be made is that, at most, nuking one city would probably suffice. There was little need for nuking the second one. Next, one could, conceivably, nuke a landmark instead of a city, prove the destructive power of the device and, still, spare a lot of lives.
No. Nuking 2 cities was more a weapons test than a way to shorten a war.